Bibounded uo-convergence and b-property in vector lattices

Alpay, Safak
Emelyanov, Eduard
Gorokhova, Svetlana
We define bidual bounded uo-convergence in vector lattices and investigate relations between this convergence and b-property. We prove that for a regular Riesz dual system ⟨ X, X∼⟩ , X has b-property if and only if the order convergence in X agrees with the order convergence in X∼ ∼.


Unbounded p-convergence in lattice-normed vector lattices
Marabeh, Mohammad A. A.; Emel’yanov, Eduard; Department of Mathematics (2017)
The main aim of this thesis is to generalize unbounded order convergence, unbounded norm convergence and unbounded absolute weak convergence to lattice-normed vector lattices (LNVLs). Therefore, we introduce the follwing notion: a net $(x_alpha)$ in an LNVL $(X,p,E)$ is said to be unbounded $p$-convergent to $x in X$ (shortly, $x_alpha$ $up$- converges to $x$) if $p(lvert x_alpha −x rvert wedge u) xrightarrow{o}0$ in $E$ for all $u ∈ X_+$. Throughout this thesis, we study general properties of $up$-converge...
uτ-Convergence in locally solid vector lattices
Dabboorasad, Yousef A M; Emel’yanov, Eduard; Department of Mathematics (2018)
We say that a net (xα) in a locally solid vector lattice (X,τ) is uτ-convergent to a vector x ∈ X if
o tau-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces
Alpay, Safak; Emelyanov, Eduard; Gorokhova, Svetlana (2022-06-01)
We investigate o tau-continuous/bounded/compact and Lebesgue operators from vector lattices to topological vector spaces; the Kantorovich-Banach operators between locally solid lattices and topological vector spaces; and the Levi operators from locally solid lattices to vector lattices. The main idea of operator versions of notions related to vector lattices lies in redistributing topological and order properties of a topological vector lattice between the domain and range of an operator under investigation...
Unbounded order convergence and the Gordon theorem#
Gorokhova, S.G.; Kutateladze, S.S. (2019-01-01)
The celebrated Gordon's theorem is a natural tool for dealing with universal completions of Archimedean vector lattices. Gordon's theorem allows us to clarify some recent results on unbounded order convergence. Applying the Gordon theorem, we demonstrate several facts on order convergence of sequences in Archimedean vector lattices. We present an elementary Boolean-Valued proof of the Gao-Grobler-Troitsky-Xanthos theorem saying that a sequence xn in an Archimedean vector lattice X is uo-null (uo-Cauchy) in ...
Geometric measures of entanglement
UYANIK, KIVANÇ; Turgut, Sadi (American Physical Society (APS), 2010-03-01)
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
Citation Formats
S. Alpay, E. Emelyanov, and S. Gorokhova, “Bibounded uo-convergence and b-property in vector lattices,” Positivity, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: